Yes, they can....in fact that’s not uncommon to say when someone is getting drunk.
"Now by this time I'm plenty high You know when your mouth a-getting dry You're plenty high Looked down the bar I say to my bartender I said look man, come down here, he got down there So what you want this time? I said look man, a-what time is it? He said the clock on the wall say three o'clock Last call for alcohol So what you need? One bourbon, one scotch, one beer”
-John Lee Hooker (as adapted by George Thorogood), “One Bourbon, One Scotch, One Beer"
Technically alcohol is a drug so I don't see why not, but in comon usage here in UK we would tend to say tipsy (mildly drunk) or drunk (or any of a large number of other words (e.g. sloshed, inebriated, wasted, p*ssed, f*cked, w*nkered) instead which is more specfic.